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103 LearnersLast updated on September 24, 2025
GCF of 6 and 28
The GCF is the largest number that can divide two or more numbers without leaving any remainder. GCF is used to share items equally, to group or arrange items, and schedule events. In this topic, we will learn about the GCF of 6 and 28.
What is the GCF of 6 and 28?
The greatest common factor of 6 and 28 is 2. The largest divisor of two or more numbers is called the GCF of the numbers. If two numbers are co-prime, they have no common factors other than 1, so their GCF is 1.
The GCF of two numbers cannot be negative because divisors are always positive.
How to find the GCF of 6 and 28?
To find the GCF of 6 and 28, a few methods are described below
- Listing Factors
- Prime Factorization
- Long Division Method / by Euclidean Algorithm
GCF of 6 and 28 by Using Listing of Factors
Steps to find the GCF of 6 and 28 using the listing of factors
Step 1: Firstly, list the factors of each number
Factors of 6 = 1, 2, 3, 6.
Factors of 28 = 1, 2, 4, 7, 14, 28.
Step 2: Now, identify the common factors of them Common factors of 6 and 28: 1, 2.
Step 3: Choose the largest factor The largest factor that both numbers have is 2.
The GCF of 6 and 28 is 2.
GCF of 6 and 28 Using Prime Factorization
To find the GCF of 6 and 28 using the Prime Factorization Method, follow these steps:
Step 1: Find the prime factors of each number
Prime Factors of 6: 6 = 2 × 3
Prime Factors of 28: 28 = 2 × 2 × 7 = 2² × 7
Step 2: Now, identify the common prime factors The common prime factor is 2.
Step 3: Multiply the common prime factors
The greatest common factor of 6 and 28 is 2.
GCF of 6 and 28 Using Division Method or Euclidean Algorithm Method
Find the GCF of 6 and 28 using the division method or Euclidean Algorithm Method. Follow these steps:
Step 1: First, divide the larger number by the smaller number
Here, divide 28 by 6 28 ÷ 6 = 4 (quotient),
The remainder is calculated as 28 - (6×4) = 4
The remainder is 4, not zero, so continue the process
Step 2: Now divide the previous divisor (6) by the previous remainder (4)
Divide 6 by 4 6 ÷ 4 = 1 (quotient), remainder = 6 - (4×1) = 2
The remainder is 2, not zero, so continue the process
Step 3: Divide the previous divisor (4) by the previous remainder (2) 4 ÷ 2 = 2 (quotient), remainder = 4 - (2×2) = 0
The remainder is zero, the divisor will become the GCF.
The GCF of 6 and 28 is 2.
Common Mistakes and How to Avoid Them in GCF of 6 and 28
Finding the GCF of 6 and 28 looks simple, but students often make mistakes while calculating the GCF. Here are some common mistakes to be avoided by the students.
Mistake 1
Listing Incorrect Factors
Students may sometimes list incorrect factors.
For example, while listing factors of 6, students may mention 5, which is incorrect. To avoid this, students should carefully divide the number and list the factors correctly.
Mistake 2
Choosing the wrong common factor
Students may sometimes select the smallest common factor instead of the largest one. To avoid this confusion, students should list all the common factors and find the greatest one.
Mistake 3
Forgetting to include 1 as a factor
Sometimes students may forget 1 as a common factor of the numbers. However, it does not affect the GCF, but it indicates an incomplete understanding of factors. Students should include 1 as a factor.
Mistake 4
Using Multiples instead of factors
Students confuse factors and multiples. In that confusion, sometimes they may write multiples instead of factors. To avoid this confusion, students should know the definitions of multiples and factors clearly.
Mistake 5
Assuming GCF is always an even number
Students may assume that the GCF of two numbers will always be an even number. But it's not true; a GCF can also be an odd number. To avoid this, students should focus on common factors rather than focusing on even and odd numbers.
Greatest Common Factor of 6 and 28 Examples
Problem 1
A gardener has 6 apple trees and 28 orange trees. She wants to plant them in equal rows with the largest number of trees in each row. How many trees will be in each row?
We should find the GCF of 6 and 28. GCF of 6 and 28 is 2.
There are 2 equal groups. 6 ÷ 2 = 3 28 ÷ 2 = 14
There will be 2 groups, and each group has 3 apple trees and 14 orange trees.
Explanation
As the GCF of 6 and 28 is 2, the gardener can make 2 groups.
Now divide 6 and 28 by 2.
Each group gets 3 apple trees and 14 orange trees.
Problem 2
A school is organizing a sports event with 6 basketballs and 28 volleyballs. They want to arrange them in rows with the same number of balls in each row, using the largest possible number of balls per row. How many balls will be in each row?
GCF of 6 and 28 is 2.
So each row will have 2 balls.
Explanation
There are 6 basketballs and 28 volleyballs.
To find the total number of balls in each row, we should find the GCF of 6 and 28.
There will be 2 balls in each row.
Problem 3
A chef has 6 kg of flour and 28 kg of sugar. He wants to divide both into bags of equal weight, using the largest possible equal weight. What should be the weight of each bag?
For calculating the longest equal weight, we have to calculate the GCF of 6 and 28.
The GCF of 6 and 28 is 2.
Each bag will weigh 2 kg.
Explanation
For calculating the longest equal weight of the bags, first we need to calculate the GCF of 6 and 28, which is 2.
The weight of each bag will be 2 kg.
Problem 4
A painter has two canvases, one 6 cm wide and the other 28 cm wide. He wants to cut them into the longest possible equal widths, without any canvas left over. What should be the width of each piece?
The painter needs the longest piece of canvas.
GCF of 6 and 28 is 2.
The longest width of each piece is 2 cm.
Explanation
To find the longest width of each piece of the two canvases, 6 cm and 28 cm respectively, we have to find the GCF of 6 and 28, which is 2 cm.
The longest width of each piece is 2 cm.
Problem 5
If the GCF of 6 and ‘b’ is 2, and the LCM is 84, find ‘b’.
The value of ‘b’ is 28.
Explanation
GCF × LCM = product of the numbers
2 × 84 = 6 × b
168 = 6b
b = 168 ÷ 6 = 28
FAQs on the Greatest Common Factor of 6 and 28
1.What is the LCM of 6 and 28?
2.Is 6 divisible by 2?
3.What will be the GCF of any two prime numbers?
4.What is the prime factorization of 28?
5.Are 6 and 28 prime numbers?
Important Glossaries for GCF of 6 and 28
- Factors: Factors are numbers that divide the target number completely. For example, the factors of 8 are 1, 2, 4, and 8.
- Multiple: Multiples are the products we get by multiplying a given number by another. For example, the multiples of 3 are 3, 6, 9, 12, and so on.
- Prime Factors: These are the factors of a number that are prime numbers and divide the given number completely. For example, the prime factors of 18 are 2 and 3.
- Remainder: The value left after division when the number cannot be divided evenly. For example, when 10 is divided by 3, the remainder is 1 and the quotient is 3.
- LCM: The smallest common multiple of two or more numbers is termed LCM. For example, the LCM of 6 and 28 is 84.
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Hiralee Lalitkumar Makwana
About the Author
Hiralee Lalitkumar Makwana has almost two years of teaching experience. She is a number ninja as she loves numbers. Her interest in numbers can be seen in the way she cracks math puzzles and hidden patterns.
Fun Fact
: She loves to read number jokes and games.
